Design and parameterization of a stochastic cellular automaton describing a chemical reaction

Abstract

Although most of the work concerned with reaction kinetics concentrates on empirical findings, stochastic models, and differential equations, a growing number of researchers is exploring other methods to elucidate reaction kinetics. In this work, the parameterization of an utter discrete spatio-temporal model, more specifically, a cellular automaton (CA), describing the reaction of HCl with CaCO(3) , is suggested. Furthermore, a system of partial differential equations (PDE), deduced from a set of CA rules, is implemented to compare both modeling paradigms. In this article, the experimental setup to acquire time series of data is explained, a stochastic CA-based model and a continuous PDE-based model capable of describing the reaction are proposed, the models are parameterized using the experimental data and, finally, the relationship between a discrete time step of the CA-based model and the physical time is studied. Essentially, the parameterization of both models can be traced back to the quest for a solution of the inverse problem in which a (set of) rule(s), respectively a system of PDE, is deduced starting from the observed data. It is demonstrated that the proposed CA- and PDE-based models are capable of describing the considered chemical reaction with a high accuracy, which is confirmed by a root mean squared error between the simulated and observed data of 0.388 and 0.869 g CO(2) , respectively. Further, it is shown that an exponential or linear relationship can be used to link the physical time to a discrete time step of the CA-based model.

A CA-Based Model Describing Fat Bloom in Chocolate

“…liquid) fat in the neighborhood is sufficiently high. This type of reaction is suited to be modeled with a CA-based model as has already been demonstrated by some of the present authors [15,16].…”

Cellular automata approach to hybrid surface and diffusion controlled reactions

“…This approach is also used by Bentz [36], based on the Knudsen Approach [42]. This challenge was addressed by Van der Weeën et al [4] by presuming a time step of 0.01 s, when coupling a cellular automata model to a partial differential equations based model. This paper intends to provide a unique direct relation between time and cycles for diffusion controlled systems as earlier done for surface controlled reactions [12], rather than the general approach given by Knudsen.…”

“…which enable the reaction simulation of arbitrary shaped and densely packed particles. Cellular automata are therefore already commonly used for the modeling of chemical systems [1][2][3][4][5][6][7][8][9][10][11]. Cellular automata systems are among others applied for studying biology, cement reaction, population growth, computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modelling.…”

A generalized cellular automata approach to modeling first order enzyme kinetics

“…A more accurate representation of processes, dependent on the behavior of a small number of molecules of relevance in both chemistry and biochemistry, can be achieved through stochastic modeling (Seybold et al 1997). In fact, the intrinsic nature of any chemical reaction is stochastic as it has been pointed out by Van der Weeën et al (2011). A local transition rule specifies a time-and space-independent probability distribution of next states for each possible neighborhood configuration.…”